Interference patterns produced by binomially splitting atom states in a double well optical lattice can be used to probe many important properties of this system, including double well tilt (and tilt inhomogeneities), the on-site interaction energy U, atom number distribution across the lattice, vibrational excitation, and lattice state coherence, making atom interferometry a powerful tool to analyze and characterize the structure and states of optical lattice systems, an essential task if they are to realize their potential for quantum information and for a variety of other proposed uses.
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